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C₂×#12008 #483334

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 42 points:

(1,2);(3,4,5,7,6,8,9,10)(11,12)(13,22)(14,19)(15,29)(16,31)(17,21)(18,25)(20,23)(24,35)(26,41)(27,37)(28,34)(30,42)(32,39)(33,40)(36,38);(11,13,23,38,16,26,30,40,17,27,28,39,14,24,15,25)(12,18,29,35,19,32,34,37,21,33,42,41,31,36,20,22);(11,14,17,16)(12,19,21,31)(13,24,27,26)(15,28,30,23)(18,32,33,36)(20,29,34,42)(22,35,37,41)(25,39,40,38)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390530);